SOLUTION: how do you solve: square root of (w-4)= square root of (-11-24) can I square both sides and solve for w?

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Question 423282: how do you solve:
square root of (w-4)= square root of (-11-24) can I square both sides and solve for w?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28w-4%29=sqrt%28-11-24%29
Before you square both sides, simplify the radicand on the right side. (The expression inside a radical is called a radicand.)
sqrt%28w-4%29=sqrt%28-36%29
With the radicand simplified we can see that it is a negative number. The square root of a negative number is what we call an imaginary number. With imaginary numbers, you should factor out a -1 and rewrite the expression in terms of "i" (which is defined to be sqrt%28-1%29 before proceeding:
sqrt%28w-4%29=sqrt%28-1%2A36%29
sqrt%28w-4%29=sqrt%28-1%29%2Asqrt%2836%29
sqrt%28w-4%29=i%2A6
or
sqrt%28w-4%29=6i

Now we can square both sides:
%28sqrt%28w-4%29%29%5E2=%286i%29%5E2
which simplifies as follows:
w-4=36i%5E2
Since i+=+sqrt%28-1%29, i%5E2+=+-1:
w-4=36%28-1%29
w-4=-36
Add 4:
w = -32

Note: You may notice that if you skip all the stuff with "i" and square both sides at the beginning like you wanted to, you end up with the same answer. While this is true for this particular problem, it will not work with every equation involving imaginary numbers. So with square root equations, you should start by checking for imaginary numbers and, if you find some, rewrite them in terms of "i" before proceeding with the rest of the problem!